Weather is the classifier used for clouds, snow and other weather related agents. Weather affects certain aspects of temperature (and other factors) of the room that it's in, such as heat and soil moisture.
C2 models water vapour released from the oceans, which then moves around the world based on prevailing winds, temperature and water content. When the conditions in the clouds are such that the water can no longer be held, it will start to precipitate as either rain or snow, depending on the temperature. Storms develop when the water content builds up to a high level and cannot precipitate. If there are no clouds left in your world, it will be because the air above the seas is too cold for water vapour to leave and form clouds. If you never see snow, but only see rain, then the world is too warm for snow to form.
In C3, the various terrariums have their own weather systems, which are controlled by the environmental control panel found in each of them. Several third-party metarooms also come with their own weather systems.